1157F · Maximum Balanced Circle

Problem: There are $n$ people in a row. The height of the $i$-th person is $a_i$. You can choose any subset of these people and try to arrange them into a balanced circle.

A balanced circle is such an order of people that the difference between heights of any adjacent people is no more than $1$. For example, let heights of chosen people be $[a_{i_1}, a_{i_2}, \dots, a_{i_k}]$, where $k$ is the number of people you choose. Then the condition $|a_{i_j} - a_{i_{j + 1}}| \le 1$ should be satisfied for all $j$ from $1$ to $k-1$ and the condition $|a_{i_1} - a_{i_k}| \le 1$ should be also satisfied. $|x|$ means the absolute value of $x$. It is obvious that the circle consisting of one person is balanced.

Your task is to choose the maximum number of people and construct a balanced circle consisting of all chosen people. It is obvious that the circle consisting of one person is balanced so the answer always exists.

Input Format: The first line of the input contains one integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of people.

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 2 \cdot 10^5$), where $a_i$ is the height of the $i$-th person.

Output Format: In the first line of the output print $k$ — the number of people in the maximum balanced circle.

In the second line print $k$ integers $res_1, res_2, \dots, res_k$, where $res_j$ is the height of the $j$-th person in the maximum balanced circle. The condition $|res_{j} - res_{j + 1}| \le 1$ should be satisfied for all $j$ from $1$ to $k-1$ and the condition $|res_{1} - res_{k}| \le 1$ should be also satisfied.